I'm not sure how to fix this scaling issue
There shouldn't be any problems achieving that but in your case you have 0-area faces around those faces you're supposed to scale, probably it will help if you select all and press W > Remove doubles or you can start from scratch.
Aside from that I'd like to add that shape - scaling faces out and corner vertices in - can be created in 1 step by selecting all and pressing Shift+Alt+S to activate To Sphere tool.